Ixabepilone and Vorinostat in Treating Patients With Metastatic Breast Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed stage IV adenocarcinoma of the breast; stable brain metastasis is allowed (not on anti-seizure or steroids for at least three months); if histological or cytological confirmation is not available/not done, patients who demonstrate metastatic disease as documented by computed tomography (CT) scan or magnetic resonance imaging (MRI), or Bone Scan may continue on study, if in the investigators clinical opinion this represents metastatic disease; also, skin disease that has not been biopsied may be used if in the investigators clinical opinion this represents metastatic disease * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 20 mm with conventional techniques or as \> 10 mm with spiral CT scan * Multiple prior chemotherapy regimens (including trastuzumab containing regimens in human epidermal growth factor receptor 2 \[Her-2\] positive patients) for metastatic disease are allowed; prior radiation therapy and/or prior hormonal therapy (will need 2 weeks wash out period prior to enrollment) are allowed * Life expectancy of greater than 6 months * Performance status: Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 * Hemoglobin \>= 9.0 g/dl * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Total bilirubin =\< 1.0 times upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 times the ULN * Creatinine =\< 1.5 times ULN * The effects of vorinostat and ixabepilone on the developing human fetus at the recommended therapeutic dose are unknown; women of childbearing potential must have a negative serum pregnancy test performed within 7 days of registration; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately and the patient will be withdrawn from the study * Female patient of childbearing potential is willing to use 2 adequate barrier methods of contraception to prevent pregnancy or agrees to abstain from heterosexual activity throughout the study, starting with visit 1 through 30 days after the last dose of study drug; adequate contraceptive methods include for example, intra-uterine device, diaphragm with spermicide, cervical cap with spermicide, or female condom with spermicide; spermicides alone are not an acceptable method of contraception * Male patient agrees to use an adequate method of contraception starting with the first dose of study drug through 30 days after the last dose of study drugs * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy, radiotherapy (must not include \>= 30% of major bone marrow containing area) or any systemic anti-cancer drugs within 4 weeks (2 weeks for Hormonal therapy) (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks * Patients may not be receiving any other investigational agents * Patients with unstable brain metastases (requirement of steroids or active seizures) are excluded from this clinical trial; patients with neurological symptoms must undergo a CT scan/MRI of the brain to asses brain metastasis * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection (\> Common Terminology Criteria for Adverse Events \[CTCAE\] grade 2), symptomatic congestive heart failure, unstable angina pectoris, myocardial infarction within the past 6 months, cardiac ventricular arrhythmias requiring anti-arrhythmic therapy, or psychiatric illness/social situations that would limit compliance with study requirements * Prior ixabepilone and/or vorinostat are not allowed * Prior valproic acid treatment for epilepsy will need 30 days wash out period prior to enrollment * Pregnant women are excluded from this study because of unknown potential teratogenesis * Human immunodeficiency virus (HIV)-positive patients are ineligible because of the potential for pharmacokinetic interactions with study drugs through the protease inhibition of the cytochrome P450 3A4 (CYP3A4); in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy * Patients with chronic hepatitis B or C are also excluded from this study * Any condition that impairs patient's ability to swallow whole pills * Any malabsorption problem * History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat or other agents used in the study (e.g. ixabepilone, cremaphor) * Any \> grade I neuropathy is contraindicated